Questions: whether each proposed multiplication or division of measurements is possible. If it is possible, write the proposed multiplication or division Is this possible? result 40 cm^2 / 0.40 m =? yes 42 g / 6.0 cm^2 =? yes no 1.0 m^4 / 1.0 m^2 =? yes

whether each proposed multiplication or division of measurements is possible. If it is possible, write the

proposed multiplication or division Is this possible? result

40 cm^2 / 0.40 m =? yes

42 g / 6.0 cm^2 =? yes no

1.0 m^4 / 1.0 m^2 =? yes

Transcript text: whether each proposed multiplication or division of measurements is possible. If it is possible, write the proposed multiplication or division Is this possible? result $\frac{40 . \mathrm{cm}^{2}}{0.40 \mathrm{~m}}=?$ yes $\frac{42 . \mathrm{g}}{6.0 \mathrm{~cm}^{2}}=?$ yes no $\frac{1.0 \mathrm{~m}^{4}}{1.0 \mathrm{~m}^{2}}=?$ yes

Solution

Solution Steps

To determine whether each proposed multiplication or division of measurements is possible, we need to check the compatibility of the units involved. If the units can be simplified or converted appropriately, the operation is possible. Then, we can perform the calculation.

For $\frac{40 \, \text{cm}^2}{0.40 \, \text{m}}$:
- Convert meters to centimeters to have consistent units.
- Perform the division.
For $\frac{42 \, \text{g}}{6.0 \, \text{cm}^2}$:
- Check if the units are compatible for division.
- Perform the division.
For $\frac{1.0 \, \text{m}^4}{1.0 \, \text{m}^2}$:
- Simplify the units.
- Perform the division.

Step 1: Evaluate $\frac{40 \, \text{cm}^2}{0.40 \, \text{m}}$

To perform the division, we first convert $0.40 \, \text{m}$ to centimeters: \[ 0.40 \, \text{m} = 0.40 \times 100 \, \text{cm} = 40.0 \, \text{cm} \] Now we can calculate: \[ \frac{40 \, \text{cm}^2}{40.0 \, \text{cm}} = 1.0 \, \text{cm} \]

Step 2: Evaluate $\frac{42 \, \text{g}}{6.0 \, \text{cm}^2}$

The units are compatible for division, so we can directly calculate: \[ \frac{42 \, \text{g}}{6.0 \, \text{cm}^2} = 7.0 \, \frac{\text{g}}{\text{cm}^2} \]

Step 3: Evaluate $\frac{1.0 \, \text{m}^4}{1.0 \, \text{m}^2}$

The units are also compatible here, allowing us to simplify: \[ \frac{1.0 \, \text{m}^4}{1.0 \, \text{m}^2} = 1.0 \, \text{m}^2 \]

Final Answer

The results for each proposed division are:

$\frac{40 \, \text{cm}^2}{0.40 \, \text{m}} = 1.0 \, \text{cm}$
$\frac{42 \, \text{g}}{6.0 \, \text{cm}^2} = 7.0 \, \frac{\text{g}}{\text{cm}^2}$
$\frac{1.0 \, \text{m}^4}{1.0 \, \text{m}^2} = 1.0 \, \text{m}^2$

Thus, the final boxed answers are: \[ \boxed{1.0 \, \text{cm}}, \quad \boxed{7.0 \, \frac{\text{g}}{\text{cm}^2}}, \quad \boxed{1.0 \, \text{m}^2} \]

Was this solution helpful?